A Cullen number is a number of the form

The first few are 3, 9, 25, 65, 161, 385, ... (Sloane's A002064).

Cullen numbers are divisible by if is a prime of the form .

The first few prime Cullen numbers occur for , 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, ... (Sloane's A005849; Rodenkirch and Ballinger; note however that the range from 1150000 to 1354828 is incompletely searched), corresponding to the numbers 3, 393050634124102232869567034555427371542904833, ... (Sloane's A050920).

Caldwell, C. K. "The Top Twenty: Cullen Primes." http://primes.utm.edu/top20/page.php?id=6.

Guy, R. K. "Cullen Numbers." §B20 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 77, 1994.

Keller, W. "New Cullen Primes." Math. Comput. 64, 1733-1741, 1995.

Leyland, P. http://research.microsoft.com/~pleyland/factorization/cullen_woodall/cw.htm.

Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 360-361, 1996.

Rodenkirch, M. and Ballinger, R. "Cullen Primes: Definition and Status." http://www.prothsearch.net/cullen.html.

Sloane, N. J. A. Sequences A002064/M2795, A005849/M5401, and A050920 in "The On-Line Encyclopedia of Integer Sequences."

CITE THIS AS:

Weisstein, Eric W. "Cullen Number." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CullenNumber.html